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Peter travels from his place to his uncle house a distance of 30km.He cycles for two thirds of the journey
before walking for the rest of the journey. If his cycling speed is 10km/hr more than the walking speed
and the whole journey took him 3hrs 20 minutes, calculate his cycling speed.
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Let x be his cycling speed in km/h; then his walking speed was (x-10) km/h.
He cycled 20 km at the speed x km/h --- hence, he spent hours for this part of the journey.
He walked 10 km at the speed (x-10) km/h --- hence, he spent hours for this part of the journey.
The total time was 3 hours 20 minutes = 3 hours = hours.
It gives you this "time equation"
+ = . (1)
To solve it, multiply both sides by 3
+ = 10. (2)
At this point, you just can easily guess the solution MENTALLY: it is x= 15 km/h.
Alternatively, you may reduce equation (1) or (2) to the standard form quadratic equation and solve it formally.
ANSWER. His cycling speed is 15 km/h.
CHECK. I will check equation (1) : = 1 + 2 = 3 + hours. ! Correct !
Solved.